The Fundamentalist Vision

A brief synoptic conclusion. When our aim is a distinctive account of ultimate reality the proper postmodal tool is that of fundamentality. With that tool we can articulate a "fundamentalist vision": an account of the fundamental nature of the facts and laws in the domain in question. This conception of the metaphysics of science fits a certain realist outlook, and undermines some forms of structuralism: nomic essentialism and structural realism (though not comparativism). But the vision faces serious challenges having to do with arbitrariness: arbitrariness in the constituents of the fundamental facts, and arbitrariness in the laws of nature.

Nomic Essentialism

According to nomic (or causal, or dispositional) essentialists, the identity of a property is tied up with its nomic role, the role it plays in the laws of nature. Modally speaking this is straightforward: a property could not have obeyed different laws. But postmodally it is unclear what it means, since it is hard to see how to state the fundamental facts without mentioning particular properties. Various ideas are considered and criticized, such as that facts about property instantiations, or property existence, or property identity, are grounded in facts about laws; and that the laws are essential to properties. The latter, it is argued, is insufficiently metaphysically specific to count as an improvement on the modal formulation.

Individuals

Various structuralists about individuals, such as ontic structural realists and ante rem mathematical structuralists, say that individuals are "just positions in structures". This chapter is a long study of what that might mean. Individuals are central to the foundations of mathematics and physics, so it is hard to see how the fundamental facts could be stated without reference to individuals. But if these fundamental facts do mention individuals, then it is hard to see how individuals are "just positions in structures". The main approaches considered are: antihaecceitism, eliminative structural realism, featureless particulars (moderate structural realism), weak discernibility, indeterminate identity, monism, generalism. Especially close attention is paid to Shamik Dasgupta's development of the final position.

Postmodal Metaphysics and Structuralism

Metaphysics is sensitive to our chosen conceptual tools. Those tools are a lens through which we view metaphysical problems; the same problems look different when we change the lens. In the 1950s the tools of choice were those of conceptual analysis. We asked: What role in our conceptual scheme do personal identity, mentality, and so forth play? In the 1970s and 80s the tools of choice became modal, and the questions were transformed: What criteria of re-identification of persons are valid in all possible worlds? Could a person have exactly the same physical features but different mental features? And in the past 15 years or so, there has been a shift to “postmodal” tools: ground, essence, and fundamentality. Now we ask: What grounds the facts of personal identity? What facts about the mind are fundamental? This shift impacts first-order debates about structuralism in the philosophy of mathematics and science.

Quantities

Quantitative properties are those that come in degrees, which we represent with numbers. A metaphysical account of quantity - in my view an account of the fundamental quantitative features - must explain the possibility of numerical representation; and such an account will have implications for the laws of nature in which quantitative properties figure. One such account is comparativism, the view that the fundamental quantitative features are comparative relations. Comparativism passes a minimum test (which certain other accounts fail): enabling strong laws of nature. But questions arise about the kinds of laws it enables. Hartry Field's insistence on "intrinsic" laws is examined, as well as David John Baker's argument that comparativism undermines determinism. In the end a pessimistic conclusion emerges: any account of the fundamental quantitative features, whether comparativist or no, seems to require unattractively arbitrary choices.

Equivalence

What is it for theories to be equivalent? Two extreme accounts are considered. According to the account I defend, equivalent theories are those that say the same thing at the fundamental level. This leads to certain uncomfortable choices: should a theory of time be based on a fundamental relation of earlier-than, or later-than? Should a metaphysics of logic including negation include also conjunction, or disjunction? These are normally regarded as paradigmatically equivalent theories, but my account cannot recognize this. According to the second extreme account, relations of equivalence need not be underwritten by a fundamental account of their common content. We can "quotient out" theoretical differences by simply saying, without explaining, that theories are equivalent. Objections are given to this account. But the more important moral is that the issue of quotienting often lies under the surface, but has profound implications across metaphysics and philosophy of physics, including the discussions of structuralism in earlier chapters.